I have a potential client which needs me to build a mobile application for iOS and Android, it should connect to a JSON REST API and show information in a game-fashion (with cute buttons, a lot of images, background music and not boring/standard forms). The application requires a 3D touchable world, which would act as a menu (although there are other 2D menus in the app).
I thought in Unity (the game engine), but the licensing prices are too high. I have 1 month to build the app, and no previous gamedev experience (I'm mainly a web developer), but I don't think that would be a serious problem (at least with Unity all seemed pretty accessible to me), the main problem might be the 3D touchable world as far as I think.
The project budget is about 2000 USD, license included, I would prefer an open source technology, but this is a personal taste.
Which technology could you recommend me to build this software?